Purse fastening system



FIG. 1 is a front view of my new, original and ornamental design for a purse fastening system;

FIG. 2 is a right side view thereof;

FIG. 3 is a top view thereof; and,

FIG. 4 is a front right perspective view thereof.

The broken line showing of a handbag is included for the purpose of illustrating environment and forms no part of the claimed design. 

The ornamental design for a purse fastening system, as shown and described. 